Here,the only stupid question is the one you don't ask.

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I've probably learned series and sequences 3 times already in high school and i still can't get the hang of it. finding the pattern where it's not just +2 or x(2/3) all the time is extremely difficult for me. For example, when the sequence is 1,3,7,13,21 it takes me ages to find out the pattern is (n+1). Am i doing something wrong or is there a shortcut? People in my class know it's (n+1) almost instantly during the lectures and i'm just sitting there baffled.

What you are trying to do, it seems, is to find a formula for a sequence of numbers. In your example, the simplest formula for the sequence 1,3,7,13,21 is n2−n+1 (assuming that you're starting with n=1). I don't know how it can be easy to find that out; it took me some work. It certainly wasn't obvious.

Just as zifyoip described, the typical strategy is to look at the differences between the #s and see if you can come up with a pattern there.

Ex:
1, 4, 10, 19, 31

Hard to see any pattern.. let's look at the differences: 3, 6, 9, 12.

Do the numbers 3, 6, 9, 12 mean anything to you? You probably recognize them as multiples of 3. If not you could look at their common difference.

Okay so now we know the numbers increase by a multiple of 3 each time. I'm assuming we're now trying to write the numbers in a sigma formula.

Then one thing you could try is re-writing the terms to reveal the pattern by using the previous term (which I have bolded):

1 = 1

4 = 1 + 3

10 = 4 + 6 = 4 = 2*3

19 = 10 + 9 = 10 + 3*3

If I expand one of these all the way then I get, for example

19 = 1 + 3 + 2 * 3 + 3 * 3

This lends itself to a series because it's a sum of multiples of 3. Since the 1 doesn't really math the pattern, I leave it outside the sigma, writing

19 = 1 + (sum from i=1 to 3 of 3 * i) = f(4)

Now I have to do some pattern matching to get a general formula. The only thing that should change is how high I'm summing. It looks like for n=4, I only summed up to 3, so we must sum up to n-1. This makes me guess

As far as going from the sum to an explicit formula, you can take advantage of the fact that the sum from i=1 to n of i is n * (n+1)/2, which means the sum from i=1 to (n-1) is (n-1) * n/2 and also factoring the 3 out of the sigma. If you didn't know that, check out this link which explains it pretty well.

This might have been overkill because it sounded like you just wanted a strategy for recognizing the pattern, but I think a full example is useful. For reference, the no-sums formula for f is